• Journal of the Korean Data and Information Science Society
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• 제27권2호
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• pp.539-548
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• 2016

This paper is a study on the multivariate CUSUM control charts using three different control statistics for monitoring covariance matrix. We get control limits and ARLs of the proposed multivariate CUSUM control charts using three different control statistics by using computer simulations. The performances of these proposed multivariate CUSUM control charts have been investigated by comparing ARLs. The purpose of control charts is to detect assignable causes of variation so that these causes can be found and eliminated from process, variability will be reduced and the process will be improved. We show that the charts based on three different control statistics are very effective in detecting shifts, especially shifts in covariances when the variables are highly correlated. When variables are highly correlated, our overall recommendation is to use the multivariate CUSUM control charts using trace for detecting changes in covariance matrix.

• 산업경영시스템학회지
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• 제42권2호
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• pp.18-27
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• 2019

The process control methods based on the statistical analysis apply the analysis method or mathematical model under the assumption that the process characteristic is normally distributed. However, the distribution of data collected by the automatic measurement system in real time is often not followed by normal distribution. As the statistical analysis tools, the process capability index (PCI) has been used a lot as a measure of process capability analysis in the production site. However, PCI has been usually used without checking the normality test for the process data. Even though the normality assumption is violated, if the analysis method under the assumption of the normal distribution is performed, this will be an incorrect result and take a wrong action. When the normality assumption is violated, we can transform the non-normal data into the normal data by using an appropriate normal transformation method. There are various methods of the normal transformation. In this paper, we consider the Box-Cox transformation among them. Hence, the purpose of the study is to expand the analysis method for the multivariate process capability index using Box-Cox transformation. This study proposes the multivariate process capability index to be able to use according to both methodologies whether data is normally distributed or not. Through the computational examples, we compare and discuss the multivariate process capability index between before and after Box-Cox transformation when the process data is not normally distributed.

• 한국정보전자통신기술학회논문지
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• 제14권1호
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• pp.22-28
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• 2021

화학공정, 기계공정, 발전소와 같은 다변량 공정은 여러 설비들이 복잡하게 연결되어 운영되기 때문에 특정 시스템에 고장이 발생하면 전체 공정에 치명적인 영향을 미칠 수 있다. 또한, 공정 데이터는 불안정한 환경에서 계측되므로, 데이터에 이상치가 포함될 가능성이 크다. 따라서 계측된 데이터의 이상치를 제거하고 시스템의 고장을 사전에 탐지할 수 있는 모니터링 기술이 필수적이다. 본 논문에서는 여러 종류의 공정에서 고장탐지를 수행하기 위해 다이나믹 공정과 다변량 공정 모델에서 생성된 데이터를 이용하였다. 다이나믹 공정은 자기회귀 특성을 가지는 공정을 모델링한 것이고 다변량 공정은 특정 센서의 고장이 발생했을 때 상황을 묘사한 공정이다. 본 논문에서는 두 공정에서 생성된 데이터에 마할라노비스 거리를 이용하여 데이터에 포함된 이상치를 제거한 후, 독립성분분석을 적용하여 고장탐지를 수행하였다. 제안된 방법의 성능 비교를 위해 기존의 단일모델 ICA와 성능을 비교하였다. 실험결과, 제안된 방법이 기존의 ICA 보다 다이나믹 공정의 바이어스 데이터의 경우에 0.84%p, 드리프트 데이터의 경우 6.82%p 성능이 개선되었다. 다변량 공정의 경우 3.78%p 성능이 개선되었으므로, 제안된 방법이 우수한 고장탐지 성능을 보였다.

• 한국멀티미디어학회논문지
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• 제17권7호
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• pp.858-865
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• 2014

In the case of system like MES, various sensors collect the data in real time and save it as a big data to monitor the process. However, if there is big data mining in distributed computing system, whole processing process can be improved. In this paper, system to analyze the cause of operation deviation was built using the big data which has been collected from deasphalting process at the two different plants. By applying multivariate statistical analysis to the big data which has been collected through MES(Manufacturing Execution System), main cause of operation deviation was analyzed. We present the example of analyzing the operation deviation of deasphalting process using the big data which collected from MES by using multivariate statistics analysis method. As a result of regression analysis of the forward stepwise method, regression equation has been found which can explain 52% increase of performance compare to existing model. Through this suggested method, the existing petrochemical process can be replaced which is manual analysis method and has the risk of being subjective according to the tester. The new method can provide the objective analysis method based on numbers and statistic.

• 응용통계연구
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• 제7권1호
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• pp.103-112
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• 1994

본 논문에서는 비정상(단위근) 시계열이 포함된 다변량 시계열 자료에서 단위근에 해당되는 계수행렬 추정량의 극한 분포가 정상시계열의 유무에 상관없이 일정하다는 것을 밝혔다. 또한 단위근만 존재하는 다변량 시계열에서 다중단위근을 검정하는 검정통계량을 제안하였다.

• 산업경영시스템학회지
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• 제30권4호
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• pp.182-189
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• 2007

Process Capability indices(PCIs) have been widely used in manufacturing industries to provide a quantitative measure of process performance. PCIs have been developed to represent process capability more exactly. The traditional process capability indices Cp, Cpk, Cpm, $Cpm^+$ have been used to characterize process performance on the basis of univariate quality characteristics. Cp, Cpk consider the process variation, Cpm considers both the process variation and the process deviation from target and $Cpm^+$ considers economic loss for the process deviation from target In the previous studies, only one designated location on each part is measured. System process capability index even though in single process, multiple measurement locations on each part are required to calculate the reliable process capability. In manufacturing industry, there is growing interest in quantitative measures of process variation under multivariate quality characteristics. The multivariate process capability index incorporates both the process variation and the process deviation from target or considers expected loss caused by the process deviation from target. In this paper, we compare various process capability indices and propose the application method of PCIs.

• 통합자연과학논문집
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• 제5권4호
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• pp.246-252
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• 2012

Multivariate cumulative sum (CUSUM) control charts for simultaneously monitoring both means and variances under multivariate normal process are investigated. Performances of multivariate CUSUM schemes are evaluated for matched fixed sampling interval (FSI) and variable sampling interval (VSI) features in terms of average time to signal (ATS), average number of samples to signal (ANSS). Multivariate Shewhart charts are also considered to compare the properties of multivariate CUSUM charts. Numerical results show that presented CUSUM charts are more efficient than the corresponding Shewhart chart for small or moderate shifts and VSI feature with two sampling intervals is more efficient than FSI feature. When small changes in the production process have occurred, CUSUM chart with small reference values will be recommended in terms of the time to signal.

• Journal of the Korean Data and Information Science Society
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• 제26권4호
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• pp.1027-1034
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• 2015

A control chart is very useful in monitoring various production process. There are many situations in which the simultaneous control of two or more related quality variables is necessary. When the joint distribution of the process variables is multivariate normal, multivariate Shewhart control charts using the function of the maximum likelihood estimator for monitoring the dispersion matrix are considered for the simultaneous monitoring of the dispersion matrix. The performances of the multivariate Shewhart control charts based on the proposed control statistic are evaluated in term of average run length (ARL). The performance is investigated in three cases, where the variances, covariances, and variances and covariances are changed respectively. The numerical results show that the performances of the proposed multivariate Shewhart control charts are not better than the control charts using the trace of the covariance matrix in the Jeong and Cho (2012) in terms of the ARLs.

• 품질경영학회지
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• 제22권1호
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• pp.66-81
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• 1994

Several sample statistics to simultaneously monitor both means and variances for multivariate quality characteristics under multivariate normal process are proposed. Performances of multivariate Shewhart schemes and cumulative sum(CUSUM) schemes are evaluated for matched fixed sampling interval(FSI) and variable sampling interval(VSI) feature. Numerical results show that multivariate CUSUM charts are more efficient than Shewhart charts for small or moderate shifts and VSI feature is more efficient than FSI feature.

• 한국컴퓨터정보학회논문지
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• 제12권4호
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• pp.201-207
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• 2007

제조업에서는 2개 이상의 상관이 있는 품질특성치를 동시에 감시하거나 관리를 하기 위한 필요성이 많이 제기되고 있다. 하지만 복수의 품질특성치를 각각 독립적으로 감시하면 판단의 오류가 발생될 수 있다. 복수의 품질특성치를 동시에 감시하고자 할 때 $X^2$ 또는 $T^2$와 같은 다변량 관리도가 사용되어질 수 있다. 본 논문에서는 다수의 품질특성치를 갖는 용해공정에서 조기에 이상 징후를 파악하기 위하여 다변량 관리도를 이용한 조기경보 시스템을 구현하였다. 용해공정에서 상관성이 있는 다수의 품질특성치를 동시에 관리하기 위해 개발된 이 모듈은 용해공정의 통계적 공정관리 활동에 효율성 및 효과성을 향상시켜 주었다.